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exam1_solutions - Exam1forPHYSICS2210...

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1 Exam 1 for PHYSICS 2210 9:30 to 10:45 am on Oct 1. 2009 Name: Score: 1) Multiple‐choice questions (30 points total, and 5 points each question). 1A) For two vectors a and b , which of the following statement is most accurate? A) a . (a x b) = 0. B) ( 2 a+b) . (a x b) = 0. C) (a- 2 b) . (a x b) = 0. D) A), B) and C) are all true. Answer: D) 1B) A particle circles clockwise around the origin at a constant speed | v o |. In plane polar coordinates, which expression for r , v , and a is correct? Note that r=| r |. Answer: D) r e θ . θ x 1 x 2 P O e r v o A) r =r e r , v=-|v o |e θ + |v o |e r , a = |v o | 2 /r e r . B) r =r e r , v=-|v o |e θ + |v o |e r , a =‐ |v o | 2 /r e r . C) r =r e r , v=-|v o |e θ , a=|v o | 2 /r e r . D) r =r e r , v=-|v o |e θ , a =‐ |v o | 2 /r e r . E) r =r e r , v=|v o |e θ , a =0.
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2 1C) Consider the rotational velocity field on a plane v = ω r e θ . We already showed that ∇ × v = 2 ω e z where e z is unit vector perpendicular to the plane. L 1 = v d r B S 1 and L 2 = v d r B S 2 are two line integrals along circles Bs1 (solid) and Bs2 (dashed), respectively, where the two circles have the same areas. Answer: B) Since the curl is a constant and two circles have the same areas, using the Stokes’ theorem, L1 = L2. 1D) A pendulum is suspended in an elevator that is descending with constant acceleration a ( ). There are three observers who are studying the motion of the
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